Massachusetts Institute of Technology - Physics Department
Physics - 8.01 Assignment #4 October 6, 1999.
It is strongly recommended that you read about a subject before it is covered in lectures.
Lecture Date Material Covered Reading
#13 Fri 10/8 Potential Energy - watch PIVoT Page 184 – 194
Energy Considerations to derive SHM - watch PIVoT Page 387 – 389
#14 Wed 10/13 Escape Velocities - Bound and Unbound Orbits - PIVoT Page 211 – 228
Circular Orbits (elliptical orbits will be discussed later Page 194 – 201
in the course). Various Forms of Energy - Power
#15 Fri 10/15 Momentum - Conservation of Momentum - watch PIVoT Page 113 – 114
Center of Mass - watch PIVoT Page 245 – 261
Due Friday, Oct 15, before 4 PM in 4-339B. Solutions will be posted on the Web Sat, Oct 16.
4.1 Air drag on very small drops. Watch PIVoT under resistive force.
We release an oil drop of radius rin air. The density of the oil is 700 kg/m3.C1and C2for 1
atmosphere air at 20◦C are 3.1×10−4(kg/m)/sec and 0.85kg/m3, respectively. How small should
the oil drop be so that the drag force is dominated by the linear term in the speed (in lectures we
called this Regime I). In this regime, the terminal velocity is mg/C1r. [mis the mass of the drop].
4.2 Drag force at very low speeds. Watch PIVoT under resistive force.
At low speeds (especially in liquids rather than gases), the drag force is proportional to the speed
rather than its square, i.e., F=−C1rv, where C1is a constant. At time t= 0, a small ball of mass
mis projected into a liquid so that it initially has a horizontal velocity of uin the +xdirection.
The initial speed in the vertical direction (y) is zero. The gravitational acceleration is g.
a) Write down the differential equations of motion in the xand ydirection.
b) What is the horizontal component of the ball’s velocity at time t?
c) What is the vertical component of the ball’s velocity at time t?
d) After how many seconds is the vertical speed 99% of its maximum value? What would that
be for the 1/4 inch steel ball bearing that we dropped in Karo Corn Syrup in lectures?
e) Answer the questions under b) and c) for the limiting case that tbecomes infinitely large.
4.3 SHO – page 405, problem 1. Watch PIVoT under simple harmonic motion.
4.4 SHO – page 405, problem 4. Watch PIVoT under simple harmonic motion.
4.5 Oscillating Spring. Watch PIVoT under simple harmonic motion.
A 3 kg mass is attached to a spring. The period of oscillation is 0.4 sec. At t= 0, the mass has a
speed of 3 m/sec towards equilibrium, and its displacement from equilibrium is 0.1 m.
a) Calculate the position of the mass for all time t > 0.
b) When will the mass first go through equilibrium; what then will be its speed, acceleration,
kinetic energy, and potential energy?
c) When will the mass first reach a turning point; what then will be its speed, acceleration,
kinetic energy, and potential energy?
4.6 Vertical Spring – page 406, problem 11.
